Total Internal Reflection
The Critical Angle ($\theta_c$) is the specific angle of incidence at which light passing from a denser medium (higher $n$) to a less dense medium (lower $n$) is refracted at exactly $90^\circ$—meaning it skims along the boundary.
If the light hits the boundary at an angle larger than the critical angle, it cannot escape the medium at all. Instead, it reflects perfectly back into the material. This phenomenon is called Total Internal Reflection (TIR).
The Foundation of Modern Communication
Total Internal Reflection is the "secret sauce" of the internet. In a fiber optic cable, pulses of light carrying data hit the edges of the glass core at angles larger than the critical angle. Because TIR is 100% efficient (no light is lost to the outside), the signal can travel for miles with almost no loss of intensity.
The Formula
Example Calculation
You want to find the critical angle for light leaving glass ($n_1 = 1.5$) and entering air ($n_2 = 1.0$).
- Divide indices: $1.0 / 1.5 \approx 0.667$.
- Take inverse sine: $\arcsin(0.667) \approx 41.8^\circ$.
Any light hitting the glass-air boundary at an angle steeper than $41.8^\circ$ will be trapped inside the glass.